The theory of Pangaea is just that- a theory. We can't prove it, nor can we prove that tectonic plates float on the mantle of the Earth. But we have evidence that strongly suggests that the continents have been slowly drifting apart.
Over time, as pictured above, we believe Pangaea separated into several different continents. Scientists believe this is why our continents seem to fit together so well. Eventually, they ended up as they are today. Evidence for this theory comes in the form of geologic patterns and fossils. Fossils from animals that could not have crossed an ocean from the same species have been found on continents separated by oceans. Geologic patterns and rocks have been observed and discovered to be incredibly similar from continent to continent as well.